Bodies do have different performance characteristics, but I have never found one to be a deal-breaker. The bodies I have liked the most were CRC Black Market (AKA The Mowhawk due to its center spine) and CRC Black Art Audi R8C. The Black Market was probably a little more stable, while the Audi was a little more aggressive and gave better high-speed steering. The new CRC bodies I have not tried yet but I have one painted up and even though it feels big and chunky I had a hard time getting it to clear all of my electronics and wires, as the back half of the cockpit is very narrow as it smooths out into the rear deck. I will probably be sticking with my old body selection.
To be honest, if your car is fast and well set up and running only 17.5, your body choice is a minor tuning choice, not make-or-break. The Strakka and TR-12 are both good choices, but if you chose one I would go with the Strakka, it looks better than the TR-12 too.